Juncker, who is also prime minister of Luxembourg, has over the past three years been at the heart of efforts to avoid a breakup of the euro, a currency used by 330 million people. He has weathered all-night meetings and early-morning press conferences with global markets hanging on his every word.
Other European Union officials offered fulsome praise for Juncker as he held his final press conference as eurogroup president.
"Jean-Claude Juncker is really one of the true and great Europeans of our time," said Klaus Regling, head of the European Stability Mechanism, the eurozone's new bailout fund.
Juncker said Monday he was relieved to step down. He also dashed hopes for a quick solution to the eurozone's latest problem, the cash-strapped Mediterranean island nation of Cyprus, which is seeking a bailout from its European partners.
He said a decision would probably be made in March.
Cyprus is seeking rescue loans of about €17 billion ($22.6 billion) -- almost equivalent to its annual gross domestic product. About €10 billion would shore up the country's ailing banks, with the remainder meant to keep the government afloat.
The bailout could push Cyprus' debt to 150 percent of gross domestic product, a level economists consider unsustainable for such a small economy.
In creditor nations such as Germany, Europe's biggest economy, the bailout has been met with skepticism amid allegations that Cypriot banks have helped launder Russian money and facilitated tax evasion.
German Finance Minister Wolfgang Schaeuble told the daily Sueddeutsche Zeitung that it was unclear whether there would be a bailout at all, because it wasn't clear if a Cypriot bankruptcy "would endanger the eurozone as a whole at all."
If Europe and the International Monetary Fund balk at bailing out Cyprus, which accounts for only 0.19 percent of the eurozone's economy, the country could face bankruptcy within months, possibly forcing it to leave the eurozone.
Moscovici hinted that Europeans wouldn't let Cyprus down, stressing that the priority must be to secure "the integrity of the eurozone."
Toby Sterling in Amsterdam contributed reporting.